Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)

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Hey everyone in this example we need to determine the corresponding frequency and units of hurts for the below wavelengths. We should recall that our units for wavelength. Lambda should be in meters. However, were given all units for a wavelength in PICO meters. So we should go ahead and recall that our prefix PICO tells us that for one PICO meter we have 10 to the negative 12 power meters. And so for part A we would write our wavelength as 8 Times 10 to the -12 Power m. We also want to recall our formula for frequency which is represented by this symbol. And we're going to recall that. It's going to be the speed of light divided by our wavelength. And we should recall that frequency is in units of hertz which are equivalent to inverse seconds. So let's go ahead and begin part A. Okay, So what we're going to have is that our frequency is equal to in our numerator, our speed of light we recall is 3.00 times 10 to the 8th Powerm/s. And then in our denominator we're going to plug in our wavelength which we converted to Times 10 to the -12 Power m. So this allows us to go ahead and cancel out our units of meters, leaving us with inverse seconds as our unit for frequency. And this gives us a value equal to 3.36 times 10 to the 17th power hurts. However, we have inverse seconds, which we can recall is equal to 3.36 times 10th of the 17th. Power hurts. And so this would be our first answer in hertz for our unit of frequency based on our given wavelength. Moving on to part B. Were given point oh 23 PICO meters were going to recall again are prefixed PICO will give us 0.23 times 10 to the negative 12 power meters as our wavelength. And so we're going to find our frequency again by taking in our numerator or speed of light, which we recall is 3.0 times 10 to the eighth power meters per second. And in our denominator plugging in that wavelength in meters. So 0.23 times 10 to the negative 12 power meters. Again, we're going to cancel our units of meters leaving us with inverse seconds. And so this gives us a value equal to 1.30 times 10 to the 22nd power inverse second. Which you recall is equivalent to 1.30 times 10 to the 22nd Power hurts. And so this would be our final answer for part B based on our given wavelength. And lastly we have part C where we're given 3 39 or 33.9 PICO meters as our wavelengths. So again for the last time are prefixed PICO will tell us that we have zero or 33 sorry 0.9 times 10 to the negative 12 power meters as our wavelength. And so we're going to find our frequency. But again in our numerator plugging in our speed of light, we recall as three point oh times 10 to the eighth power meters per second. And then in our denominator we're going to plug in that wavelength that we found as three or 33.9 times 10 to the negative 12 power meters. So now we can cancel out our units of meters. We're left with inverse seconds. Again in our denominator and we're going to get a value Equal to 8.8 five times 10 to the 18th power inverse seconds. Which again are equal to 8.85 times 10 to the 18th power hurts. And so this would be our final answer for our frequency based on our given wavelength. And so everything boxed in blue represents all of our final answers corresponding to the multiple choice a in our question. So I hope everything I went through is clear. If you have any questions, please leave them down below. And I will see everyone in the next practice video

Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)

Verified Solution

Key Concepts

Electromagnetic Spectrum

Wavelength and Frequency Relationship

Unit Conversion